“Unrecaptured section 1250 gain" is a very confusing term, but it really means recapturing the depreciation of 1250 property (real estate).  

So why isn't it just called "section 1250 recapture"?  Technically, that only refers to property that used accelerated depreciation.  But section 1250 property hasn't been eligible for accelerated depreciation since the mid 80s, so you may have section 1250 recapture if it's an old property that they have owned for a long time.  But these days you usually only have these two types of depreciation recapture:

• “Unrecaptured section 1250 gain":  For real property that didn't use accelerated depreciation.  Taxed at your ordinary income tax rate, but capped at a maximum of 25%. 
• "Section 1245 recapture":  For everything else.  Taxed at your ordinary income tax rate, with no upper limit.